> No one likes scaling factors to their identities. Sure, I totally agree. Doing things this way would make some things more intuitive (Hz would "work right")

> No one likes scaling factors to their identities. Sure, I totally agree. Doing things this way would make some things more intuitive (Hz would "work right") and some thing harder. As you point out, the identity e^(ix) = cos(x) + i*sin(x) would need to be rewritten e^(ix) = cos(x/2pi) + i*sin(x/2pi) or equivalently e^(ix) = cos(x radians) + i*sin(x radians) if we redefined `sin` and `cos` to take "revolutions" instead of radians. It's obviously worse in that regard -- it's longer to write, less intuitive, more difficult to work with etc. It's probably a horrible idea. It's not wrong, though. It even has some nice properties: sin(x) = -sin(x + 0.5) sin(x) = sin(x + 1) etc.